Theorems · Theorem · general topology
Filter.atTop_basis_Ioi
∀ {α : Type u_3} [inst : Preorder α] [IsDirectedOrder α] [Nonempty α] [NoMaxOrder α],
Filter.atTop.HasBasis (fun x => True) Set.Ioi- Defined in
- Mathlib.Order.Filter.AtTopBot.Basic
- Cited by
- 10 results in Mathlib
- Foundations
- Depth 65 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Preorderstatement and proof · cited by 7,952
- Filter.atTopstatement · cited by 2,405
- Set.Ioistatement · cited by 1,463
- Filter.HasBasisstatement · cited by 604
- NoMaxOrderstatement and proof · cited by 340
- IsDirectedOrderstatement and proof · cited by 316
- NoMaxOrder.exists_gtproof · cited by 62
- Filter.atTop_basisproof · cited by 42
- Filter.HasBasis.to_hasBasisproof · cited by 40
- Set.Ioi_subset_Ici_selfproof · cited by 34
- Set.Ici_subset_Ioiproof · cited by 15
Cited by10
Results whose statement or proof uses this declaration.
- Real.tendsto_exp_div_pow_atTopproof · cited by 3
- Filter.atTop_basis_Ioi'proof · cited by 2
- ENNReal.tendsto_coe_nhds_topproof · cited by 2
- WithTop.tendsto_coe_atTopproof · cited by 1
- EReal.tendsto_coe_nhds_top_iffproof · cited by 1
- Filter.frequently_atTop'proof · cited by 1
- spectrum.eventually_isUnit_resolventproof · cited by 0
- ENNReal.tendsto_rpow_at_topproof · cited by 0
- NormedAddCommGroup.tendsto_atTop'proof · cited by 0
- Metric.tendsto_atTop'proof · cited by 0